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The nonsubsampled Contourlet transform (NSCT) not only retains the characteristics of Contourlet transform, but also has the good characteristic of shift-invariance, which plays a significant role in denoising, fusion, and segmentation of texture-rich images. The NSCT not only retains the properties of Contourlet transform, but also has the important property of shift-invariance, which plays a significant role in image processing, such as denoising, fusion, and segmentation of texture-rich images. This paper proposes a Gaussian-Cauchy mixture distribution-based NSCT hidden Markov tree model (GC-NSCT-HMT). The specific form of Gaussian-Cauchy mixture distribution is determined by the kurtosis of the NSCT coefficients in each subband. First, we study the probability density distribution of the remote sensing image NSCT coefficients and then propose the Gaussian-Cauchy mixture distribution, which can adaptively adjust according to the statistical property of NSCT coefficients through a balance function. Experimental results show that the proposed mixture distribution can achieve a good imitative effect to the NSCT coefficients. Second, we study the marginal statistical property and the joint statistical property of the NSCT coefficients, the persistence and aggregation properties of them are also studied in depth. We find that the &#x2018;father&#x2019; NSCT coefficient can transfers to its son coefficients through a tree structure. Third, we combine the above conclusions with the hidden Markov tree model (HMT) and the GC-NSCT-HMT model is proposed. Finally, we apply our model to remote sensing image denoising. The subjective and objective experimental results demonstrate the feasibility of the proposed method.

The NSCT-HMT Model of Remote Sensing Image Based on Gaussian-Cauchy Mixture Distribution